2-distance 20-coloring of planar graphs with maximum degree 6

A 2-distance k-coloring of a graph G is a proper k-coloring such that any two vertices at distance two or less get different colors. The 2-distance chromatic number of G is the minimum k such that G has a 2-distance k-coloring, denoted by χ₂(G). In this paper, we show that χ₂(G) ≤ 20 for every planar graph G with maximum degree at most six, which improves a former bound χ₂(G) ≤ 21.